The Mathematics of Social Networks

In this lecture Philippa (Pip) Pattison describes how mathematical approaches have been used to build understanding of the structure of human social networks and their properties.  Social networks can reflect social and economic ties of many types, such as who-socialises-with-whom, who-collaborates-with-whom, or who-offers-credit-to-whom.  Starting with the simplest assumption of a social network as a random graph, Pip explains how the interplay between mathematical and empirical studies of networks has led to progressively more sophisticated and effective models.  A number of case examples illuminate the trajectory of model development and illustrate that a key to successful progress has been to allow for endogenous local processes in the formation and dissolution of network ties.  Pip also points to ways in which the current modelling suite can advance our understanding of some important social outcomes and then touch briefly on active areas of further model development.